1. Technical Field
The subject matter described here generally relates to fluid reaction surfaces with specific blade structures, and, more particularly, to wind turbines having blade planforms with twisted and tapered tips.
2. Related Art
A wind turbine is a machine for converting the kinetic energy in wind into mechanical energy. If the mechanical energy is used directly by the machinery, such as to pump water or to grind wheat, then the wind turbine may be referred to as a windmill. Similarly, if the mechanical energy is converted to electricity, then the machine may also be referred to as a wind generator or wind power plant.
Wind turbines are typically categorized according to the vertical or horizontal axis about which the blades rotate. One so-called horizontal-axis wind generator is schematically illustrated in FIG. 1 and available from General Electric Company. This particular configuration for a wind turbine 2 includes a tower 4 supporting a nacelle 6 enclosing a drive train 8. The blades 10 are arranged on a hub to form a “rotor” at one end of the drive train 8 outside of the nacelle 6. The rotating blades 10 drive a gearbox 12 connected to an electrical generator 14 at the other end of the drive train 8 arranged inside the nacelle 6 along with a control system 16 that receives input from an anemometer 18.
The blades 10 generate lift and capture momentum from moving air that is them imparted to a rotor as the blades spin in the “rotor plane.” Each blade is typically secured at its “root” end, and then “rotor radiuss” radially “outboard” to a free, “tip” end. The front, or “leading edge,” of the blade connects the forward-most points of the blade that first contact the air. The rear, or “trailing edge.” of the blade is where airflow that has been separated by the leading edge rejoins after passing over the suction and pressure surfaces of the blade. A “chord line” connects the leading and trailing edges of the blade in the direction of the typical airflow across the blade. The length of the chord line is simply the “chord.”
The outboard ends of the blades 10 are called “tips” and the distance from the tip to the root, at the opposite end of the blade, is called the “rotor radius.” Since the root of the blade 10 is displaced from the blade's center of rotation when it is connected to the hub, the distance from the center of rotation of the blade 10 to tip is referred to as the “rotor radius” and designated here with the letter “R.” Since many blades 10 change their chord over the span (and corresponding rotor radius), the chord length is referred to as the “root chord,” near the root, and the “tip chord,” near the tip of the blade. The resulting shape of the blade 10, when viewed perpendicular to the direction of flow, is called the “planform.” The thickness of a blade 10 varies across the planform, and the term “thickness” is typically used to describe the maximum distance between the low pressure suction surface and the high pressure surface on the opposite side of the blade for any particular chord line.
“Angle of attack” is a term that is used in to describe the angle between the chord fine of the blade 10 and the vector representing the relative motion between the blade and the air. “Pitching” refers to rotating the angle of attack of the entire blade 10 into or out of the wind in order to control the rotational speed and/or absorption of power from the wind. For example, pitching the blade “towards feather” rotates of the leading edge of the blade 10 into the wind, while pitching the blades “towards stall” rotates the leading edge of the blade out of the wind.
Since the speed of the blades 10 relative to air increases along the rotor radius of the rotating blades, the shape of the blades is typically twisted in order to maintain a generally consistent angle of attack at most points along the rotor radius of the blade. For example, FIG. 2 illustrates a conventional blade twist distribution 20 showing the “twist” angle θ of the blades 10 in degrees on the vertical axis. The horizontal axis in FIG. 2 shows the normalized distance outward from the center of rotation of blade 10 along the span, “r/R,” referred to here as “percent of rotor radius” or “normalized rotor radius.” Due to the relatively small size of the hub as compared to the length of the blades 10, this “percent of rotor radius” may also be approximated as the normalized distance outward starting from the root of the blade, or “percent of span,” rather than starting from the center of rotation of the blade.
Positive values of twist angle θ in these figures indicate that the blade 10 is twisted towards feather, while negative values indicate that the blade is twisted toward stall. The twist angle θ generally staffs with a high positive (towards feather) value inboard and then “rotates” towards stall in the outboard direction along the rotor radius of the blade. This change is called “forward twist” of the blade. When the twist angle is rotated towards feather the change is called “backward twist.” A zero value for twist angle θ indicates that portion of the blade 10 will be in the rotor plane when the blade is arranged on the rotor 8 with zero pitch.
FIG. 3 is an enlarged portion of the twist distribution 20 shown in FIG. 2, where the entire blade 10 has also been pitched forward. Since FIG. 3 shows the twist distribution of an outer portion of the blade 10 near the tip, it is also referred to as a “tip twist distribution.” FIG. 3 corresponds to the following numerical data:
r/Rθ - 2096.00%−1.6396.80%−1.6897.40%−1.6698.06%−1.6298.56%−1.5499.06%−1.3599.56%−0.58100.00%1.67However, other tip twist distributions have also been published. For example, “Design of Tapered and Twisted Blade for the NREL Combined Experiment Rotor,” Publication No. NREL/SR-500-26173 (April 1999) illustrates a twist distribution which is negative from about 75% of rotor radius to the blade tip.
The noise and power performance of wind turbine blades 10 depends, in part, upon vortex development at the tip of the blade. Various techniques have been proposed to control this vortex development. For example, commonly-owned co-pending U.S. application Ser. No. 11/827,532 filed on Jul. 12, 2007 discloses a wind turbine blade having a vortex breaking system for reducing noise. While vortex development can generally be reduced by minimizing the aerodynamic load at the tip of the blade, so-called “tip unloading” typically causes a significant reduction in power that is produced by the blade.
The drawbacks and advantages of such tip unloading can also be achieved by decreasing the chord near the tip. For example, FIG. 7 is a plot of chord “c” as a percentage of total rotor radius “R” (also referred to as “c/R” or “normalized chord”) versus normalized rotor radius for the conventional turbine blade discussed above with respect to FIGS. 2 and 3. The “tip chord distribution” 22 illustrated in FIG. 7 corresponds to the following data:
r/Rc/R - 2295.56%1.95%96.00%1.94%96.80%1.92%97.40%1.90%98.06%1.88%98.56%1.85%99.06%1.79%99.56%1.52%100.00%0.70%
FIG. 9 is a plot of chord “c” as a percentage of total rotor radius “R” (also referred to as “c/R” or “normalized chord”) for the leading and trailing edges of the blade tip verses normalized rotor radius for the conventional turbine blade discussed above and shown in FIGS. 2, 3 and 7. The resulting “tip planform distribution” or plan view of the contour of the blade tip corresponds to the following data where the zero value for c/R has been arbitrarily attributed to the pitch axis of the blade:
r/Rc/R(24)c/R(25)95.56%0.60%−1.35%96.00%0.60%−1.34%96.80%0.59%−1.33%97.40%0.58%−1.32%98.06%0.57%−1.31%98.56%0.55%−1.30%99.06%0.53%−1.25%99.56%0.39%−1.13%100.00%0.00%−0.70%
The values for c/R in plot 24 correspond to the leading edge (LE) of the blade while the values in plot 25 correspond to the trailing edge (TE) of the blade. A zero value for c/R is assigned to the center point of the pitch rotation on the chord at every rotor radiuswise location. It can be assigned to any other points of intersection between a line along the blade and the chord at every rotor radius location by adding or subtracting the appropriate amount from all of the c/R chord values.